Get Correct Texture from Object
You need to bake the texture:

Create a second UV map without overlapping. Create new image texture (press New in the UV / Image Editor view) and add it to your material node setup. Connect the new UV map to this texture vector slot using the Input / UV Map node, or in older versions of blender the Input / Attribute node. Select the new texture, so it becomes the active texture. Now you can bake texture to the second map, and then save it from the UV / Image Editor view.